標題: Equivalence between Clar covering polynomials of single zigzag chains and tiling polynomials of 2 x n rectangles
作者: Langner, Johanna
Witek, Henryk A.
應用化學系
應用化學系分子科學碩博班
Department of Applied Chemistry
Institute of Molecular science
關鍵字: Kekule structure;Clar structure;Perfect matching;Zhang-Zhang polynomial;Interface;Tiling
公開日期: 10-Jul-2018
摘要: This paper offers a formal explanation of a rather puzzling and surprising equivalence between the Clar covering polynomials of single zigzag chains and the tiling polynomials of 2 x n rectangles for tilings using 1 x 2, 2 x 1 and 2 x 2 tiles. It is demonstrated that the set of Clar covers of single zigzag chains N(n - 1) is isomorphic to the set of filings of a 2 x n rectangle. In particular, this isomorphism maps Clar covers of N(n - 1) with k aromatic sextets to tilings of a 2 x n rectangle using k square 2 x 2 tiles. The proof of this fact is an application of the recently introduced interface theory of Clar covers. The existence of a similar relationship between the Clar covers of more general benzenoid structures and more general tilings of rectangles remains an interesting open problem in chemical graph theory. (C) 2018 Elsevier B.V. All rights reserved.
URI: http://dx.doi.org/10.1016/j.dam.2018.02.019
http://hdl.handle.net/11536/145124
ISSN: 0166-218X
DOI: 10.1016/j.dam.2018.02.019
期刊: DISCRETE APPLIED MATHEMATICS
Volume: 243
起始頁: 297
結束頁: 303
Appears in Collections:Articles